A spherical Hopfield model

Details A spherical Hopfield model A spherical Hopfield model

2003-05-14

arxiv.org/abs/cond-mat/0305316v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

9 pages Latex including 3 eps figures, Addition of an author in the HTML-abstract unintentionally forgotten, no changes to the

Scientific paper

10.1088/0305-4470/36/41/002

We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynamics and dynamics of this model. In order to have a retrieval phase a quartic term is added to the Hamiltonian. The thermodynamics of the model is exactly solvable and the results are replica symmetric. A Langevin dynamics leads to a closed set of equations for the order parameters and effective correlation and response function typical for neural networks. The stationary limit corresponds to the thermodynamic results. Numerical calculations illustrate our findings.

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